2002 AMC 12A Problems/Problem 22
Problem
Triangle is a right triangle with as its right angle, , and . Let be randomly chosen inside , and extend to meet at . What is the probability that ?
Solution
Clearly and . Choose a and get a corresponding such that and . For we need , creating an isosceles right triangle with hypotenuse . Thus the point may only lie in the triangle . The probability of it doing so is the ratio of areas of to , or equivalently, the ratio of to because the triangles have identical altitudes when taking and as bases. This ratio is equal to . Thus the answer is .
See Also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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